Trim radishes and cut lengthwise into 1/2-inch wedges.
Heat 1 1/2 tablespoons butter in a 12-inch heavy skillet over moderately high heat until foam subsides, then saute radish wedges with salt, stirring, until crisp-tender, about 12 minutes. Transfer to a platter and keep warm, loosely covered.
Saute garlic in remaining tablespoon butter in skillet over moderately high heat, stirring, until fragrant, about 30 seconds. Add watercress and saute, covered, until wilted, about 2 to 3 minutes. Return radish wedges to skillet to reheat quickly and serve.